Problem: Simplify the following expression and state the condition under which the simplification is valid. $a = \dfrac{n^2 - 16}{n - 4}$
First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = n$ $ b = \sqrt{16} = -4$ So we can rewrite the expression as: $a = \dfrac{({n} {-4})({n} + {4})} {n - 4} $ We can divide the numerator and denominator by $(n - 4)$ on condition that $n \neq 4$ Therefore $a = n + 4; n \neq 4$